具有正向性的有簇玻雷阿诺索夫表征

Pub Date : 2024-03-06 DOI:10.1007/s10711-024-00895-2

Gye-Seon Lee, Tengren Zhang

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引用次数: 0

摘要

我们证明，如果一个从晶格 \(\Gamma \subset \textsf{PGL}_2({{\,\mathrm{\mathbb {R}}\})\) 到 \(\textsf{PGL}_d({{\、\)的图象中包含一个具有单个乔丹块的单能元，那么它必然是一个（尖顶）希金表示。我们还证明了希钦表示与非希钦的尖顶玻雷尔阿诺索夫表示的合并从来都不是尖顶玻雷尔阿诺索夫表示。

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Cusped Borel Anosov representations with positivity

We show that if a cusped Borel Anosov representation from a lattice \(\Gamma \subset \textsf{PGL}_2({{\,\mathrm{\mathbb {R}}\,}})\) to \(\textsf{PGL}_d({{\,\mathrm{\mathbb {R}}\,}})\) contains a unipotent element with a single Jordan block in its image, then it is necessarily a (cusped) Hitchin representation. We also show that the amalgamation of a Hitchin representation with a cusped Borel Anosov representation that is not Hitchin is never cusped Borel Anosov.

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